It's probably not impossible (though certainly not easy). But in any case it's not worth it because of the sheer damage to legitimacy and public faith in this country's political system which would take place if we avoided any form of leaving.
The people who won the Leave vote - people, just to be clear, who I think are profoundly wrong about a lot of things - haven't been listened to for decades, and going so far out of our way to ignore them once again will not make the UK less divided or make the country more harmonious or stable. Even with the finest set of laws in the world, democracy will only ever work if people actually feel invested in it, and like their votes genuinely mean anything. If they don't, it's a recipe for serious dysfunction and collapse.
If the government wrangle out of Brexit (something I feel will be a disaster, but hey ho) then our whole political system will undergo a serious legitimacy crisis that will have profound consequences lasting decades. I don't know exactly what this would look like, but I'm not sure the UK's vibrant political culture would ever recover. Which even next to the worst predictions for Brexit is probably not a price worth paying.